Stosur, who won the U.S. Open last year, was beaten by Cirstea 7-6 (7-2), 6-3. Cirstea had five breaks, with three coming in the second set. Stosur had 33 unforced errors against just 12 winners.
Stosur was the only seeded player to lose Tuesday but it wasn't such a good day for the Australians. Jelena Dokic was a 6-2, 6-1 winner over Anna Chakvetadze but countrywomen Jarmila Gajdosova and Isabella Holland joined Stosur on the sidelines, leaving Australian players 1-3 on the day.
Second-seeded Petra Kvitova and No. 4 Maria Sharapova lost just three games between them in sweeping out of the first round.
Kvitova was on the court 61 minutes in dispatching Vera Dushevina 6-2, 6-0 behind six breaks in seven receiving games. Sharapova needed just 58 minutes to finish off a 6-0, 6-1 romp over Gisela Dulko. Sharapova won 69 percent of the points in the match, taking near three-quarters of the points when Dulko served.
Seventh-seeded Vera Zvonareva survived a 7-6 (7-4), 6-7 (5-7), 6-3 scare from Alexandra Dulgheru while No. 9-seeded Marion Bartoli topped Virginie Razzano 7-5, 6-0. Serena Williams, seeded 12th, won the last three games of the first set and last four of the second in a 6-3, 6-2 win over Tamira Paszek.
No. 14-seeded Sabine Lisicki needed a third set to get by Stefanie Voegele 6-2, 4-6, 6-4 and 15th-seeded Anastasia Pavlyuchenkova beat Klara Zakopalova 7-6 (7-5), 6-1.
Other seeded players advancing to the second round were No. 17 Dominika Cibulkova, 18th-seeded Svetlana Kuznetsova, No. 23 Roberta Vinci, 25th-seeded Kaia Kanepi, No. 17 Maria Kirilenko, 29th-seeded Nadia Petrova and 30th-seeded Angelique Kerber.
In addition to Dokic, unseeded players winning Tuesday were Shahar Peer, Sara Errani, Lucie Hradecka, Ekaterina Makarova, Carla Suarez Navarro, Vania King, Michaella Krajicek, Greta Arn, Sloane Stephens, Stephanie Dubois, Urszula Radwanska, Aleksandra Wozniak and Jamie Hampton.
Celebrity Families of 2014 [PHOTOS]